Question

Rank of an identity matrix of order 4 is

Answer 1

SOLUTION

TO DETERMINE

Rank of an identity matrix of order 4

CONCEPT TO BE IMPLEMENTED

Let A be a non zero matrix of order m × n. The Rank of A is defined to be the greatest positive integer r such that A has at least one non-zero minor of order r

For a non-zero m × n matrix A

0 < rank of A ≤ min {m, n}

For a non-zero matrix A of order n,

rank of A < , or = n according as A is singular or non-singular

EVALUATION

Here the given matrix is identity matrix

Since the identity matrix is a non-singular matrix

So rank of an identity matrix of order 4 = 4

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